a domain registrar
You cannot just declare that example.com is yours — names have to be allocated so two people do not claim the same one. A domain registrar is the company you go through to register and rent a domain name. Think of it as the ticket counter for names: you tell the registrar which name you want, they check it is free and let you reserve it, and you pay a yearly fee to keep it. Familiar registrars are the sites where people buy domains.
There are three roles to keep straight. A registry is the organization that operates a top-level domain and holds the master database of names within it (for example, the operator of all .com names). A registrar is an accredited company that takes your order and submits registrations to the registry on your behalf. And you are the registrant — the person or organization that holds the name. When you register, the registrar records who you are and, importantly, which name servers are authoritative for your domain, so DNS can find your records. You typically rent in yearly terms and must renew, or the name can expire and become available to others.
Why it matters: the registrar is your control panel for a domain's existence — through it you set your authoritative name servers (pointing the world at where your DNS lives), transfer the domain, renew it, and protect it. A few honest cautions: registration is a rental, not permanent ownership, so a lapsed renewal can cost you the name; the registrar is a separate concern from your DNS hosting (some registrars also host your zone, but you can use a different DNS provider); and registrar account security matters a great deal, because whoever controls the registrar account can redirect or hijack the entire domain.
You register example.com through a registrar for one year. In its control panel you set the authoritative name servers to ns1.dnsprovider.net and ns2.dnsprovider.net — the registry now points the world at those servers, and your DNS records start resolving worldwide.
Registry runs the TLD; the registrar takes your order; you are the registrant.
Registering a domain is renting it, not owning it forever; let the renewal lapse and you can lose the name. Also keep the registrar account well secured — control of it means control of the whole domain.